Fingered growth in channel geometry: A Loewner equation approach

Abstract

A simple model of Laplacian growth is considered, in which the growth takes place only at the tips of long, thin fingers. In a recent paper, Carleson and Makarov used the deterministic Loewner equation to describe the evolution of such a system. We extend their approach to a channel geometry and show that the presence of the side walls has a significant influence on the evolution of the fingers and the dynamics of the screening process, in which longer fingers suppress the growth of the shorter ones.

References in corpus (4)

• A Guide to Stochastic Loewner Evolution and its Applications
• The Loewner equation: maps and shapes
• Exact Solutions for Loewner Evolutions
• Diffusion-limited aggregation in channel geometry